Computation of the posterior, or approximations to it, is the focus of data assimilation. The posterior provides the optimal estimate of the state of the system, representing the distribution of model states that are most consistent with the observations. In practical geophysical examples, it is not possible to fully characterise the posterior distribution, and different data assimilation methodologies are used to infer certain properties of the posterior e.g. its mean, mode, or variance [1]}, [2]}. A particle filter is set of a data assimilation methodologies that aims to approximate the full posterior distribution via an ensemble of "particles" [3]}, [4]}, [5]}, [6]}, [7]}, [8]}.
